Do you have anything specific in mind? I think the term integrability is sometimes used in slightly different contexts.
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Pieter NaaijkensSep 22 '11 at 12:25

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The fact that "integrability" can mean so many things sometimes makes the quest to learn about it so challenging! I have found the introductory sections of Etingoff's paper www-math.mit.edu/~etingof/zlecnew.pdf to be a very good mathematical reference for a particular, physically interesting system (Calogero-Moser) which describes particles interacting in one-dimension.
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Eric ZaslowSep 24 '11 at 17:28